Prime obsession : Bernhard Riemann and the greatest unsolved problem in mathematics

The Riemann hypothesis is a conjecture which has resisted attempts to prove it for a century and a half, and so is of great interest to the mathematical community. In 'Prime Obsession' John Derbyshire takes a dual approach to this topic, alternating mathematical chapters with chapters on the Riemann's life and the history of the hypothesis. I think that this works extremely well - if you are finding the maths hard going, then you have a break with a historical chapter (and vice-versa of course). I feel that it is a structure which other authors would do well to consider applying to their subject.

The structure of the book also means that the maths can proceed independently of the history. Other books have a tendency to give a superficial coverage of the nature of the hypothesis early on. In this book the subject is dealt with more gradually, to give a fuller appreciation of link between prime numbers and the zeroes of the complex valued zeta function. The book is aimed at the non-technical reader, but I feel that to reach the end of the book you will really need to be reasonably comfortable with mathematics, at least up to the later parts of school mathematics.